Based on the WMAP data,
the assumption of spatial isotropy
was questioned in Ref. [1]},
where the authors pointed at the anomalous alignment of the CMB quadrupole
and octopole (at the level \(1/60\) )
(for a recent review of CMB anomalies, see Ref. [2]}).
The authors of Ref. [1]} pointed out that
the Universe with toroidal topology could explain such an alignment
(albeit other features of this model were absent in the data); but
they did not attempt geometric explanations.
Later Refs. [4]}, [5]}
found no evidence for toroidal topology in the Planck satellite data.
Land and Magueijo [6]}, [7]}, [8]}
further worked out the ideas in Ref. [1]},
and pointed out that the Universe
may have a preferred axis, which approximately corresponds to
that of the
CMB dipole, suggesting that on very large scales the Universe
violates spatial isotropy.
Given that the WMAP observations of low multipoles were precise enough, the Planck data have not brought deep new insights
into this question, see e.g. Refs. [10]}
and [11]}. The Planck team
is cautious regarding whether statistical anomalies
in the CMB are real or just a statistical fluke:
“The existence of these features is uncontested, but,
given the modest significances at which they deviate from
the standard \(\Lambda \) CDM cosmological model, and the
a posteriori nature of their detection, the extent to which they provide evidence for a violation of isotropy in the CMB remains
unclear. It is plausible that they are indeed simply statistical fluctuations.”
However, recent LSS data tend to corroborate
the CMB data. For example, in his recent essay,
Peebles [12]} takes a more positive
view on the anomalies, regarding them as tantalizing
hints for new, as-yet-undisclosed physics. In particular,
in section 3, Peebles considers anomalies in
large scale structures, and remarks: “The measured
dipoles in the distribution of quasars and in the distributions of radio
galaxies cataloged at several radio frequencies are in about the predicted direction, but the dipole amplitudes are too large, an anomaly,”
for details see
Refs. [13]}, [14]}, [15]}, [16]}.
Peebles also mentions some other (more local) anomalies, including
the local void.
For a more comprehensive overview of the existing anomalies
in \(\Lambda \) CDM
(which include the Hubble and \(\sigma _8\)  tensions)
see Refs. [17]}, [2]}
and [19]}.
